From the signal processing point of view, the nondifferentiable data defined on the Cantor sets are investigated in this paper. The local fractional Fourier series is used to process the signals, which are the local fractional continuous functions. Our results can be observed as significant extensions of the previously known results for the Fourier series in the framework of the local fractional calculus. Some examples are given to illustrate the efficiency and implementation of the present method.

In this paper, we suggest the series expansion method for finding the series solution for the time-fractional diffusion equation involving Caputo fractional derivative.

Yang-Laplace transforms is an alternative approach to nonlinear fractional equations with local fractional derivative and local fractional integral. This paper presents a new wave equation with local fractional derivative. Finally, by using the Yang-Laplace transforms, its solution to nonlinear fractional wave equation is investigated in detail.